Species’ Distribution Modeling for Conservation
Educators and Practitioners
Richard G. Pearson
Center for Biodiversity and Conservation & Department of Herpetology
American Museum of Natural History
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ABSTRACT ..............................................................................................................3
LEARNING OBJECTIVES .....................................................................................3
PART A: INTRODUCTION AND THEORY ........................................................................4
1. INTRODUCTION ................................................................................................4
WHAT IS A SPECIES’ DISTRIBUTION MODEL? ........................................................4
2. THEORETICAL FRAMEWORK...............................................................................8
GEOGRAPHICAL VERSUS ENVIRONMENTAL SPACE................................................8
ESTIMATING NICHES AND DISTRIBUTIONS ..........................................................11
USES OF SPECIES’ DISTRIBUTION MODELS ........................................................15
PART B: DEVELOPING A SPECIES’ DISTRIBUTION MODEL .............................................17
3. DATA TYPES AND SOURCES .............................................................................17
BIOLOGICAL DATA ...........................................................................................19
ENVIRONMENTAL DATA ...................................................................................21
4. MODELING ALGORITHMS .................................................................................22
DIFFERENCES BETWEEN METHODS AND SELECTION OF ‘BEST’ MODELS ................27
5. ASSESSING PREDICTIVE PERFORMANCE ...........................................................28
STRATEGIES FOR OBTAINING TEST DATA ...........................................................28
THE PRESENCE/ABSENCE CONFUSION MATRIX ..................................................30
SELECTING THRESHOLDS OF OCCURRENCE ......................................................34
THRESHOLD-INDEPENDENT ASSESSMENT .........................................................37
CHOOSING A SUITABLE TEST STATISTIC ............................................................39
PART C: CASE STUDIES ..........................................................................................40
CASE STUDY 1: PREDICTING DISTRIBUTIONS OF KNOWN AND UNKNOWN SPECIES IN
MADAGASCAR (BASED ON RAXWORTHY ET AL., 2003)............................................40
CASE STUDY 2: SPECIES’ DISTRIBUTION MODELING AS A TOOL FOR PREDICTING
INVASIONS OF NON-NATIVE PLANTS (BASED ON THUILLER ET AL., 2005) ..................41
CASE STUDY 3: MODELING THE POTENTIAL IMPACTS OF CLIMATE CHANGE ON SPECIES’
DISTRIBUTIONS IN BRITAIN AND IRELAND (BASED ON BERRY ET AL., 2002) ...............43
ACKNOWLEDGEMENTS ...........................................................................................44
REFERENCES ........................................................................................................44
Species’ Distribution Modeling for Conservation
Educators and Practitioners
Richard G. Pearson
Center for Biodiversity and Conservation & Department of Herpetology
American Museum of Natural History
ABSTRACT
Models that predict distributions of species by combining known occurrence
records with digital layers of environmental variables have much potential for
application in conservation. Through using this module, teachers will enable
students to develop species’ distribution models, to apply the models across a
series of analyses, and to interpret predictions accurately. Part A of the synthesis
introduces the modeling approach, outlines key concepts and terminology, and
describes questions that may be addressed using the approach. A theoretical
framework that is fundamental to ensuring that students understand the uses and
limitations of the models is then described. Part B of the synthesis details the
main steps in building and testing a distribution model. Types of data that can be
used are described and some potential sources of species’ occurrence records
and environmental layers are listed. The variety of alternative algorithms for
developing distribution models is discussed, and software programs available to
implement the models are listed. Techniques for assessing the predictive ability
of a distribution model are then discussed, and commonly used statistical tests
are described. Part C of the synthesis describes three case studies that illustrate
applications of the models: i) Predicting distributions of known and unknown
species in Madagascar; ii) Predicting global invasions by plants of South African
origin; and iii) Modeling the potential impacts of climate change on species’
distributions in Britain and Ireland.
This synthesis document is part of an NCEP (Network of Conservation Educators
and Practitioners; http://ncep.amnh.org/) module that also includes a
presentation and a practical exercise:
•
An introduction to species distribution modeling: theory and practice
(presentation by Richard Pearson)
•
Species distribution modeling using Maxent (practical by Steven Phillips)
This module is targeted at a level suitable for teaching graduate students and
conservation professionals.
Learning objectives
Through use of this synthesis, teachers will enable students to
1. Understand the theoretical underpinnings of species’ distribution models
2. Run a distribution model using appropriate data and methods
3. Test the predictive performance of a distribution model
4. Apply distribution models to address a range of conservation questions
PART A: INTRODUCTION AND THEORY
1. INTRODUCTION
Predicting species’ distributions has become an important component of
conservation planning in recent years, and a wide variety of modeling techniques
have been developed for this purpose (Guisan and Thuiller, 2005). These models
commonly utilize associations between environmental variables and known
species’ occurrence records to identify environmental conditions within which
populations can be maintained. The spatial distribution of environments that are
suitable for the species can then be estimated across a study region. This
approach has proven valuable for generating biogeographical information that
can be applied across a broad range of fields, including conservation biology,
ecology and evolutionary biology. The focus of this synthesis is on conservationoriented applications, but the methods and theory discussed are also applicable
in other fields (see Table 1 for a list of some uses of species’ distribution models
in conservation biology and other disciplines).
This synthesis aims to provide an overview of the theory and practice of species’
distribution modeling. Through use of the synthesis, teachers will enable students
to understand the theoretical basis of distribution models, to run models using a
variety of approaches, to test the predictive ability of models, and to apply the
models to address a range of questions. Part A of the synthesis introduces the
modeling approach and describes the usefulness of the models in addressing
conservation questions. Part B details the main steps in building a distribution
model, including selecting and obtaining suitable data, choosing a modeling
algorithm, and statistically assessing predictive performance. Part C of the
synthesis provides three case studies that demonstrate uses of species’
distribution models.
What is a species’ distribution model?
The most common strategy for estimating the actual or potential geographic
distribution of a species is to characterize the environmental conditions that are
suitable for the species, and to then identify where suitable environments are
distributed in space. For example, if we are interested in modeling the distribution
of a plant that is known to thrive in wet clay soils, then simply identifying locations
with clay soils and high precipitation can generate an estimate of the species’
distribution. There are a number of reasons why the species may not actually
occupy all suitable sites (e.g. geographic barriers that limit dispersal, competition
from other species), which we will discuss later in this Synthesis. However, this is
the fundamental strategy common to most distribution models.
The environmental conditions that are suitable for a species may be
characterized using either a mechanistic or a correlative approach. Mechanistic
models aim to incorporate physiologically limiting mechanisms in a species’
tolerance to environmental conditions. For example, Chuine and Beaubien
(2001) modeled distributions of North American tree species by estimating
responses to environmental variables (including mean daily temperature, daily
precipitation, and night length) using mechanistic models of factors including frost
injury, phenology, and reproductive success. Such mechanistic models require
detailed understanding of the physiological response of species to environmental
factors and are therefore difficult to develop for all but the most well understood
species.
Correlative models aim to estimate the environmental conditions that are suitable
for a species by associating known species’ occurrence records with suites of
environmental variables that can reasonably be expected to affect the species’
physiology and probability of persistence. The central premise of this approach is
that the observed distribution of a species provides useful information as to the
environmental requirements of that species. For example, we may assume that
our plant species of interest favors wet clay soils because it has been observed
growing in these soils. The limitations of this approach are discussed later in the
synthesis, but it has been demonstrated that this method can yield valuable
biogeographical information (e.g., Bourg et al., 2005; Raxworthy et al., 2003).
Since spatially explicit occurrence records are available for a large number of
species, the vast majority of species’ distribution models are correlative. The
correlative approach to distribution modeling is the focus of this synthesis.
The principal steps required to build and validate a correlative species’
distribution model are outlined in Figure 1. Two types of model input data are
needed: 1) known species’ occurrence records; and 2) a suite of environmental
variables. ‘Raw’ environmental variables, such as daily precipitation records
collected from weather stations, are often processed to generate model inputs
that are thought to have a direct physiological role in limiting the ability of the
species to survive. For example, Pearson et al. (2002) used a suite of seven
climate variables and five soil variables to generate five model input variables,
including maximum annual temperature, minimum temperature over a 20-year
period, and soil moisture availability. At this stage care should be taken to ensure
that data are checked for errors. For example, simply plotting the species’
occurrence records in a GIS can help identify records that are distant from other
occupied sites and should therefore be checked for accuracy. Data types and
sources are discussed in detail in Section 3.
Figure 1. Flow diagram detailing the main steps required for building and validating a correlative species distribution model.
The species occurrence records and environmental variables are entered into an
algorithm that aims to identify environmental conditions that are associated with
species occurrence. If just one or two environmental variables were used, then
this task would be relatively straightforward. For example, we may readily
discover that our plant species has only been recorded at localities where mean
monthly precipitation is above 60mm and soil clay content is above 40%. In
practice, we usually seek algorithms that are able to integrate more than two
environmental variables, since species are in reality likely to respond to multiple
factors. Algorithms that can incorporate interactions among variables are also
preferable (Elith et al. 2006). For example, a more accurate description of our
plant’s requirements may be that it can occur at localities with mean monthly
precipitation between 60mm and 70mm if soil clay content is above 60%, and in
wetter areas (>70mm) if clay content is as low as 40%.
A number of modeling algorithms that have been applied to this task are
reviewed in Section 4. Depending on the method used, various decisions and
tests will need to be made at this stage to ensure the algorithm gives optimal
results. For example, a suitable ‘regularization’ parameter will need to be
selected if applying the Maxent method (see Phillips et al. 2006, and Box 3), or
the degrees of freedom must be selected if running a generalized additive model
(see Guisan et al. 2002). The relative importance of alternative environmental
predictor variables may also be assessed at this stage so as to select which
variables are used in the final model.
Having run the modeling algorithm, a map can be drawn showing the predicted
species’ distribution. The ability of the model to predict the known species’
distribution should be tested at this stage. A set of species occurrence records
that have not previously been used in the modeling should be used as
independent test data. The ability of the model to predict the independent data is
assessed using a suitable test statistic. Different approaches to generating test
datasets and alternative statistical tests are discussed in Section 5. Since a
number of modeling algorithms predict a continuous distribution of environmental
suitability (i.e. a prediction between 0 and 1, as opposed to a binary prediction of
‘suitable’ or ‘unsuitable’), it is sometimes useful to convert model output into a
prediction of suitable (1) or unsuitable (0). This is a necessary step before
applying many test statistics; thus, methods for setting a threshold probability,
above which the species is predicted as present, are also outlined in Section 5.
Once these steps have been completed, and if model validation is successful,
the model can be used to predict species’ occurrence in areas where the
distribution is unknown. Thus, a set of environmental variables for the area of
interest is input into the model and the suitability of conditions at a given locality
is predicted. In many cases the model is used to ‘fill the gaps’ around known
occurrences (e.g., Anderson et al., 2002a; Ferrier et al., 2002). In other cases,
the model may be used to predict species’ distributions in new regions (e.g. to
7
study invasion potential, for review see Peterson, 2003) or for a different time
period (e.g. to estimate the potential impacts of future climate change, for review
see Pearson and Dawson, 2003). Three examples of the use of predictions from
species distribution models are presented in Part C. Ideally, model predictions
into different regions of for different time periods should be tested against
observed data; for example, Thuiller et al. (2005; see case study 2) tested
predictions of invasion potential using occurrence records from the invaded
distribution, whilst Araújo et al. (2005a) tested predictions of distribution shifts
under climate change using observed records from different decades.
This modeling approach has been variously termed ‘species distribution’,
‘ecological niche’, ‘environmental niche’, ‘habitat suitability’ and ‘bioclimate
envelope’ modeling. Use of the term ‘species distribution modeling’ is widespread
but it should be noted that the term is somewhat misleading since it is actually
the distribution of suitable environments that is being modeled, rather than the
species’ distribution per se. Regardless of the name used, the basic modeling
process is essentially the same (see Part B) and the theoretical underpinnings of
the models are similar. It is essential that these theoretical underpinnings are
properly understood in order to interpret model outputs accurately. The following
section describes this theoretical framework.
2. THEORETICAL FRAMEWORK
This section outlines some of the fundamental concepts that are crucial for
understanding how species’ distribution models work, what types of questions
they are suitable for addressing, and how model output should be interpreted.
Geographical versus environmental space
We are used to thinking about the occurrence of species in geographical space;
that is, the species’ distribution as plotted on a map. To understand species’
distribution models it is important to also think about species occurring in
environmental space, which is a conceptual space defined by the environmental
variables to which the species responds. The concept of environmental space
has its foundations in ecological niche theory. The term ‘niche’ has a long and
varied history of use in ecology (Chase and Leibold, 2003), but the definition
proposed by Hutchinson (1957) is most useful in the current context. Hutchinson
defined the fundamental niche of a species as the set of environmental
conditions within which a species can survive and persist. The fundamental niche
may be thought of as an ‘n-dimensional hypervolume’, every point in which
corresponds to a state of the environment that would permit the species to exist
indefinitely (Hutchinson, 1957, p. 416). It is the axes of this n-dimensional
hypervolume that define environmental space.
Visualizing a species’ distribution in both geographical and environmental space
helps us to define some basic concepts that are crucial for species’ distribution
modeling (Fig. 2). Notice that the observed localities constitute all that is known
8
about the species’ actual distribution; the species is likely to occur in other areas
in which it has not yet been detected (e.g., Fig. 2, area A). If the actual
distribution is plotted in environmental space then we identify that part of
environmental space that is occupied by the species, which we can define as the
occupied niche.
Figure 2. Illustration of the relationship between a hypothetical species’ distribution in
geographical space and environmental space. Geographical space refers to spatial location as
commonly referenced using x and y coordinates. Environmental space refers to Hutchinson’s ndimensional niche, illustrated here for simplicity in only two dimensions (defined by two
environmental factors, e1 and e2). Crosses represent observed species occurrence records. Grey
shading in geographical space represents the species’ actual distribution (i.e. those areas that
are truly occupied by the species). Notice that some areas of actual distribution may be unknown
(e.g. area A is occupied but the species has not been detected there). The grey area in
environmental space represents that part of the niche that is occupied by the species: the
occupied niche. Again, notice that the observed occurrence records may not identify the full
extent of the occupied niche (e.g. the shaded area immediately around label D does not include
any known localities). The solid line in environmental space depicts the species’ fundamental
niche, which represents the full range of abiotic conditions within which the species is viable. In
geographical space, the solid lines depict areas with abiotic conditions that fall within the
fundamental niche; this is the species’ potential distribution. Some regions of the potential
distribution may not be inhabited by the species due to biotic interactions or dispersal limitations.
For example, area B is environmentally suitable for the species, but is not part of the actual
distribution, perhaps because the species has been unable to disperse across unsuitable
environments to reach this area. Similarly, the non-shaded area around label C is within the
species’ potential distribution, but is not inhabited, perhaps due to competition from another
species. Thus, the non-shaded area around label E identifies those parts of the fundamental
niche that are unoccupied, for example due to biotic interactions or geographical constraints on
species dispersal.
9
The distinction between the occupied niche and the fundamental niche is similar,
but not identical, to Hutchinson’s (1957) distinction between the realized niche
and the fundamental niche. With reference to the case of two species utilizing a
common resource, Hutchinson described the realized niche as comprising that
portion of the fundamental niche from which a species is not excluded due to
biotic competition. The definition of the occupied niche used in this synthesis
broadens this concept to include geographical and historical constraints resulting
from a species’ limited ability to reach or re-occupy all suitable areas, along with
biotic interactions of all forms (competition, predation, symbiosis and parasitism).
Thus, the occupied niche reflects all constraints imposed on the actual
distribution, including spatial constraints due to limited dispersal ability, and
multiple interactions with other organisms.
If the environmental conditions encapsulated within the fundamental niche are
plotted in geographical space then we have the potential distribution. Notice that
some regions of the potential distribution may not be inhabited by the species
(Fig. 2, areas B and C), either because the species is excluded from the area by
biotic interactions (e.g., presence of a competitor or absence of a food source),
because the species has not dispersed into the area (e.g., there is a geographic
barrier to dispersal, such as a mountain range, or there has been insufficient time
for dispersal), or because the species has been extirpated from the area (e.g.
due to human modification of the landscape).
Before we go on to discuss how these concepts are used in distribution
modeling, it is important to appreciate that the environmental variables used in a
distribution model are unlikely to define all possible dimensions of environmental
space. Hutchinson originally proposed that all variables, “both physical and
biological” (1957, p.416), are required to define the fundamental niche. However,
the variables available for modeling are likely to represent only a subset of
possible environmental factors that influence the distribution of the species.
Variables used in modeling most commonly describe the physical environment
(e.g. temperature, precipitation, soil type), though aspects of the biological
environment are sometimes incorporated (e.g. Araújo and Luoto 2007, Heikkinen
et al. 2007). However, the distinction between biotic and abiotic variables is often
problematic; for example, land cover type is likely to incorporate both abiotic (e.g.
urban) and biotic (e.g. deciduous forest) classes.
Another important factor that we must be aware of is source-sink dynamics,
which may cause a species to be observed in unsuitable environments. ‘Sourcesink’ refers to the situation whereby an area (the ‘sink’) may not provide the
necessary environmental conditions to support a viable population, yet may be
frequently visited by individuals that have dispersed from a nearby area that does
support a viable population (the ‘source’). In this situation, species occurrence
may be recorded in sink areas that do not represent suitable habitat, meaning
that the species is present outside its fundamental niche (Pulliam, 2000). We can
logically expect this situation to occur most frequently in species with high
10
dispersal ability, such as birds. In such cases it is useful to only utilize records for
modeling that are known to be from breeding distributions, rather than migrating
individuals. Because correlative species distribution models utilize observed
species occurrence records to identify suitable habitat, inclusion of occurrence
localities from sink populations is problematic. However, it is often assumed that
observations from source areas will be much more frequent than observations
from sink areas, so this source of potential error is commonly overlooked.
One more thing to be aware of before we move on is that some studies explicitly
aim to only investigate one part of the fundamental niche, by using a limited set
of predictor variables. For example, it is common when investigating the potential
impacts of future climate change to focus only on how climate variables impact
species’ distributions. A species’ niche defined only in terms of climate variables
may be termed the climatic niche (Pearson and Dawson, 2003), which
represents the climatic conditions that are suitable for species existence. An
approximation of the climatic niche may then be mapped in geographical space,
giving what is commonly termed the bioclimate envelope (Huntley et al., 1995;
Pearson and Dawson, 2003).
Estimating niches and distributions
Let us now consider the extent to which species’ distribution models can be used
to estimate the niche and distribution of a species. We will assume in this section
that the model algorithm is excellent at defining the relationship between
observed occurrence localities and environmental variables; this will enable us to
focus on understanding the ecological assumptions underlying distribution
models. The ability of different modeling algorithms to identify the relationship
between occurrence localities and environmental variables is discussed in
Section 4.
Let us first ask what the aim of the modeling is: what element of a species’
distribution are we trying to estimate? There are many potential uses of the
approach (Table 1) and these require modeling either the actual distribution or
the potential distribution. For example, if a model is being used with the purpose
of selecting sites that should be given high conservation priority, then modeling
the actual distribution will be the aim (since there would be less priority given to
conserving sites where the environment is suitable for the species, but the
species is not present). In contrast, if the purpose is to identify sites that may be
suitable for the reintroduction of an endangered species, then modeling the
potential distribution is an appropriate aim. We will now consider the degree to
which alternative aims are achievable using the species’ distribution modeling
approach.
11
Table 1. Some published uses of species’ distribution models in conservation biology
Type of use
Guiding field surveys to find populations of
known species
Guiding field surveys to accelerate the
discovery of unknown species
Projecting potential impacts of climate
change
Predicting species’ invasion
Exploring speciation mechanisms
Supporting conservation prioritization and
reserve selection
Species delimitation
Assessing the impacts of land cover
change on species’ distributions
Testing ecological theory
Comparing paleodistributions and
phylogeography
Guiding reintroduction of endangered
species
Assessing disease risk
Example reference(s)
Bourg et al. 2005, Guisan et al. 2006
Raxworthy et al. 2003
Iverson and Prasad 1998, Berry et al.
2002, Hannah et al. 2005; for review
see Pearson and Dawson 2003
Higgins et al. 1999, Thuiller et al. 2005; for
review see Peterson 2003
Kozak and Wiens 2006, Graham et al.
2004b
Araújo and Williams 2000, Ferrier et al.
2002, Leathwick et al. 2005
Raxworthy et al. 2007
Pearson et al. 2004
Graham et al. 2006, Anderson et al. 2002b
Hugall et al. 2002
Pearce and Lindenmayer 1998
Peterson et al. 2006, 2007
Based in part on Guisan and Thuiller 2005.
Correlative species’ distribution models rely on observed occurrence records for
providing information on the niche and distribution of a species. Two key factors
are important when considering the degree to which observed species
occurrence records can be used to estimate the niche and distribution of a
species:
1) The degree to which the species is at ‘equilibrium’ with current
environmental conditions. A species is said to be at equilibrium with the
physical environment if it occurs in all suitable areas, while being absent
from all unsuitable areas. The degree of equilibrium depends both on
biotic interactions (for example, competitive exclusion from an area) and
dispersal ability (organisms with higher dispersal ability are expected to be
closer to equilibrium than organisms with lower dispersal ability; Araújo
and Pearson, 2005). When using the concept of ‘equilibrium’ we should
remember that species distributions change over time, so the term should
not be used to imply stasis. However, the concept is useful for us here to
help understand that some species are more likely than others to occupy
areas that are abiotically suitable.
2) The extent to which observed occurrence records provide a sample of the
environmental space occupied by the species. In cases where very few
12
occurrence records are available, perhaps due to limited survey effort
(Anderson and Martinez-Meyer, 2004) or low probability of detection
(Pearson et al., 2007), the available records are unlikely to provide a
sufficient sample to enable the full range of environmental conditions
occupied by the species to be identified. In other cases, surveys may
provide extensive occurrence records that provide an accurate picture as
to the environments inhabited by a species in a particular region (for
example, breeding bird distributions in the United Kingdom and Ireland are
well known; Gibbons et al., 1993). It should be noted that there is not
necessarily a direct relationship between sampling in geographical space
and in environmental space. It is quite possible that poor sampling in
geographical space could still result in good sampling in environmental
space.
Each of these factors should be carefully considered to ensure appropriate use of
a species’ distribution model (see Box 1). In reality, species are unlikely to be at
equilibrium (as illustrated by area B in Fig. 2, which is environmentally suitable
but is not part of the actual distribution) and occurrence records will not
completely reflect the range of environments occupied by the species (illustrated
by that part of the occupied niche that has not been sampled around label D in
Fig. 2). Fig. 3 illustrates how a species’ distribution model may be fit under these
circumstances. Notice that the model is calibrated (i.e. built) in environmental
space and then projected into geographical space. In environmental space, the
model identifies neither the occupied niche nor the fundamental niche; instead,
the model fits only to that portion of the niche that is represented by the observed
records. Similarly, the model identifies only some parts of the actual and potential
distributions when projected back into geographical space. Therefore, it should
not be expected that species’ distribution models are able to predict the full
extent of either the actual distribution or the potential distribution.
This observation may be regarded as a failure of the modeling approach
(Woodward and Beerling, 1997; Lawton, 2000; Hampe, 2004). However, we can
identify three types of model prediction that yield important biogeographical
information: species’ distribution models may identify 1) the area around the
observed occurrence records that is expected to be occupied (Fig. 3, area 1); 2)
a part of the actual distribution that is currently unknown (Fig. 3, area 2); and/or
3) part of the potential distribution that is not occupied (Fig. 3, area 3). Prediction
types 2 and 3 can prove very useful in a range of applications, as we will see in
the following section.
13
Figure 3. Diagram illustrating how a hypothetical species’ distribution model may be fitted to
observed species occurrence records (using the same hypothetical case as in Fig. 2). A
modelling technique (e.g. GARP, Maxent) is used to characterize the species’ niche in
environmental space by relating observed occurrence localities to a suite of environmental
variables. Notice that, in environmental space, the model may not identify either the species’
occupied niche or fundamental niche; rather, the model identifies only that part of the niche
defined by the observed records. When projected back into geographical space, the model will
identify parts of the actual distribution and potential distribution. For example, the model
14
projection labeled 1 identifies the known distributional area. Projected area 2 identifies part of the
actual distribution that is currently unknown; however, a portion of the actual distribution is not
predicted because the observed occurrence records do not identify the full extent of the occupied
niche (i.e. there is incomplete sampling; see area D in Fig. 2). Similarly, modeled area 3 identifies
an area of potential distribution that is not inhabited (the full extent of the potential distribution is
not identified because the observed occurrence records do not identify the full extent of the
fundamental niche due to, for example, incomplete sampling, biotic interactions, or constraints on
species dispersal; see areas D and E in Fig. 2).
Uses of species’ distribution models
Consider modeled area 2 in Fig. 3, which identifies part of the actual distribution
for which no occurrence records have been collected. Although the model does
not predict the full extent of the actual distribution, additional sampling in the area
identified may yield new occurrence records. A number of studies have
demonstrated the utility of species’ distribution modeling for guiding field surveys
toward regions where there is an increased probability of finding new populations
of a known species (Fleishman et al., 2002; Bourg et al., 2005; Guisan et al.,
2006; also see Case Study 1). Accelerating the discovery of new populations in
this way may prove extremely useful for conservation planning, especially in
poorly known and highly threatened landscapes.
Consider now predicted area 3 in Fig. 3. Here, the model identifies an area of
potential distribution that is environmentally similar to where the species is known
to occur, but which is not inhabited. The full extent of the potential distribution is
not predicted, but the model can be useful for identifying sites that may be
suitable for reintroduction of a species (Pearce and Lindenmayer, 1998) or sites
where a species is most likely to become invasive (if it overcomes dispersal
barriers and if biotic competition does not prevent establishment; Peterson,
2003). Model predictions of this type also have the potential to accelerate the
discovery of previously unknown species that are closely related to the modeled
species and that occupy similar environmental space but different geographical
space (Raxworthy et al., 2003; see Case Study 1).
Model predictions as illustrated in Fig. 3 therefore have the potential to yield
useful information, even though species are not expected to inhabit all suitable
locations and sampling may be poor. Additional uses of species’ distribution
modeling include identifying potential areas for disease outbreaks (Peterson et
al., 2006), examining niche evolution (Peterson et al., 1999; Kozak and Wiens,
2006) and informing taxonomy (Raxworthy et al., 2007). However, some potential
applications require an estimation of the actual distribution of a species. For
example, if a model is being used with the purpose of selecting priority sites for
conservation, then an estimate of the actual species’ distribution is desired since
it would be inefficient to conserve sites where the species is not present (Loiselle
et al., 2003). In such cases, it should be remembered that modeled distributions
represent environmentally suitable regions but do not necessarily correspond
closely with the actual distribution. Additional processing of model output may be
required to improve predictions of the actual distribution. For example, predicted
areas that are isolated from observed occurrence records by a dispersal barrier
15
may be removed (Peterson et al., 2002) and the influence of competing species
may be incorporated (Anderson et al., 2002b).
It is useful to note that mechanistic distribution models (e.g., Chuine and
Beaubien, 2001) are subject to the same basic caveat as correlative approaches:
the models aim to identify areas with suitable environmental conditions, but do
not inform us which areas are actually occupied. Mechanistic models are ideally
suited to identifying a species’ fundamental niche, and hence its potential
distribution. This is because mechanistic approaches model physiological
limitations in a species’ environmental tolerance, without relying on known
occurrence records to define suitable environments. However, the detailed
understanding of species’ physiology that is required to build mechanistic models
prohibits their use in many instances.
The discussion in this section should help clarify the theoretical basis of the
species’ distribution modeling approach. It is crucial that any application of these
models has a sound theoretical basis and that model outputs are interpreted in
the context of this framework (see Box 1). It should now be apparent why the
terminology used to describe these models is so varied throughout the literature.
The terms ‘ecological niche model’, ‘environmental niche model’, ‘bioclimate
envelope model’ and ‘environmental suitability model’ usually refer to attempts to
estimate the potential distribution of a species. Use of the term ‘species
distribution model’ implies that the aim is to simulate the actual distribution of the
species. Nevertheless, each of these terms refers to the same basic approach,
which can be summarized as follows: 1) the study area is modeled as a raster
map composed of grid cells at a specified resolution, 2) the dependent variable is
the known species’ distribution, 3) a suite of environmental variables are collated
to characterize each cell, 4) a function of the environmental variables is
generated so as to classify the degree to which each cell is suitable for the
species (Hirzel et al., 2002). Part B of this synthesis details the principal steps
required to build a distribution model, including selecting and obtaining suitable
data, choosing a modeling algorithm, and statistically assessing predictive
performance.
16
Box 1. Caution! On the use and misuse of models
Garbage in, garbage out: This old adage is as relevant to distribution
modeling as it is to other fields. Put simply, a model is only as good as the
data it contains. Thus, if the occurrence records used to build a correlative
species’ distribution model do not provide useful information as to the
environmental requirements of the species, then the model cannot provide
useful output. If you put garbage into the model, you will get garbage out.
Model extrapolation: ‘Extrapolation’ refers to the use of a model to
make predictions for areas with environmental values that are beyond the
range of the data used to calibrate (i.e. develop) the model. For example,
suppose a distribution model was calibrated using occurrence records that
spanned a temperature range of 10–20oC. If the model is used to predict
the species’ distribution in a different region (or perhaps under a future
climate scenario) where the temperature reaches 25oC, then the model is
extrapolating. In this case, because the model has no prior information
regarding the probability of the species’ occurrence at 25oC, the prediction
may be extremely uncertain (see Pearson et al., 2006). Model
extrapolation should be treated with a great deal of caution.
The lure of complicated technology: Many approaches to modeling
species’ distributions utilize complex computational technology (e.g.
machine learning tools such as artificial neural networks and genetic
algorithms) along with huge GIS databases of digital environmental layers.
In some cases, these approaches can yield highly successful predictions.
However, there is a risk that model users will be swayed by the apparent
complexity of the technology: ‘it is so complicated, it must be correct’!
Always remember that a model can only be useful if the theoretical
underpinnings on which it is based are sound.
For additional discussion of the limitations of ecological models, see
the NCEP module Applications of remote sensing to ecological modeling.
PART B: DEVELOPING A SPECIES’ DISTRIBUTION MODEL
3. DATA TYPES AND SOURCES
Correlative species’ distribution models require two types of data input: biological
data, describing the known species’ distribution, and environmental data,
describing the landscape in which the species is found. This section discusses
the types of data that are suitable for distribution modeling, and reviews some
possible sources of data (see Table 2).
Data used for distribution modeling are usually stored in a Geographical
Information System (GIS; see Box 2). The data may be stored either as point
localities (termed ‘point vector’ data; e.g. sites where a species has been
observed, or locations of weather stations), as polygons defining an area (termed
‘polygon vector’ data; e.g. areas with different soil types) or as a grid of cells
17
(termed ‘raster’ data; e.g. land cover types derived from remote sensing [see
NCEP module Remote sensing for conservation biology]). For use in a
distribution model, it is usual to reformat all environmental data to a raster grid.
For example, temperature records from weather stations may be interpolated to
give continuous data over a grid (Hijmans et al. 2005). Formatting all data to the
same raster grid ensures that environmental data are available for every cell in
which biological data have been recorded. These cells, containing both biological
data and environmental data, are used to build the species’ distribution model.
After the model is constructed, its fit to test occurrence records is evaluated (see
section 5) and, if the fit is judged to be acceptable, the occurrence of species in
cells for which only environmental data are available can be predicted. Note that
in some applications the model may be used to predict the species’ distribution in
a region from which data were not used to build the model (e.g. to predict the
spread of an invasive species) or under a future climate scenario. In these cases,
environmental data for the new region or climate scenario must also be collated.
Table 2. Some example sources of biological and environmental data for use in species’
distribution modeling.
Type of data
Species’ distributions
- Data for a wide range of organisms in
many regions of the world
- Data for a range of organisms,
mostly rare or endangered, and
primarily in North America
Climate
- Interpolated climate surfaces for the
globe at 1km resolution
- Scenarios of future climate change
for the globe
- Reconstructed palaeoclimates
Topography
- Elevation and related variables for
the globe at 1km resolution
Source
Global Biodiversity Information Facility
(GBIF): www.gbif.org
NatureServe:
www.NatureServe.org
WorldClim:
http://www.worldclim.org/
Intergovernmental Panel on Climate
Change (IPCC): http://www.ipcc-data.org/
NOAA:
http://www.ncdc.noaa.gov/paleo/paleo.html
USGS:
http://edc.usgs.gov/products/elevation/
gtopo30/hydro/index.html
Remote sensing (satellite)
- Various land cover datasets
Global Landcover Facility:
http://glcf.umiacs.umd.edu/data/
- Various atmospheric and land
NASA:
products from the MODIS instrument http://modis.gsfc.nasa.gov/data/
Soils
- Global soil types
UNEP:
http://www.grid.unep.ch/data/data.php?
category=lithosphere
Marine
- Various datasets describing the
NOAA:
world’s oceans
www.nodc.noaa.gov
18
A consideration when collating data is the spatial scale at which the model will
operate. Spatial scale has two components: extent and resolution (see NCEP
module Applications of remote sensing to ecological modeling). Extent refers to
the size of the region over which the model is run (e.g. New York state or the
whole of North America) whilst resolution refers to the size of grid cells (e.g. 1km2
or 10km2). Note that it is common for datasets with large extent to have coarse
resolution (e.g. data for North America at 10km2) and datasets with small extent
to have fine resolution (e.g. New York state at 1km2). Spatial scale can play an
important role in the application of a species’ distribution model. In particular,
ideally the data resolution should be relevant to the species under consideration:
the appropriate data resolution for studying ants is likely to be very different from
that for studying elephants.
Box 2. The Role of Geographic Information Systems (GIS)
GIS is a vital tool in species’ distribution modeling. The large
datasets of biological and environmental data that are used in distribution
modeling are ideally suited to being stored, viewed and formatted in a
GIS. For example, useful GIS operations include changing geographic
reference systems (it is essential that all data are referenced to a common
coordinate system, so occurrence records can be matched with the
environmental conditions at the site), reformatting spatial resolution, and
interpolating point locality data to a grid. GIS is also crucial for visualizing
model results and carrying out additional processing of model output, such
as removing predicted areas that are isolated from observed species
records by a dispersal barrier (Peterson et al., 2002). However, the
distribution modeling itself is usually undertaken outside the GIS
framework. With few exceptions (e.g. Ferrier et al. 2002), the distribution
model does not ‘see’ geographical coordinates; instead, the model
operates in environmental space (see Section 2). Some GIS platforms
now incorporate distribution modeling tools (e.g. DIVA GIS: www.divagis.org/, IDRISI: http://www.clarklabs.org/), or have add-in scripts that
enable distribution models to be run (e.g. BIOCLIM script for ArcView:
http://arcscripts.esri.com/details.asp?dbid=13745), but running the model
within a GIS is not necessary.
Biological data
Data describing the known distribution of a species may be obtained in a variety
of ways:
1) Personal collection: occurrence localities can be obtained during field
surveys by an individual or small group of researchers. For example,
Fleishman et al. (2001) built models using butterfly occurrence records
collected by the researchers during surveys in Nevada, USA.
19
2) Large surveys: distribution information may be available from surveys
undertaken by a large number of people. For example, Araújo et al.
(2005a) built distribution models using data from The new atlas of
breeding birds in Britain and Ireland: 1988-1991 (Gibbons et al., 1993),
which represents the sampling effort of hundreds of volunteers.
3) Museum collections: occurrence localities can be obtained from
collections in natural history museums. For example, Raxworthy et al.
(2003) utilized occurrence records of chameleons in Madagascar that are
held in museum collections.
4) Online resources: distributional data from a variety of sources are
increasing being made available over the internet (see Table 2). For
example, the Global Biodiversity Information Facility (www.gbif.org) is
collating available datasets from a diversity of sources and making the
information available online via a searchable web portal.
Species distribution data may be either presence-only (i.e. records of localities
where the species has been observed) or presence/absence (i.e. records of
presence and absence of the species at sampled localities). Different modeling
approaches have been developed to deal with each of these cases (see Section
4). In some instances, the inclusion of absence records has been shown to
improve model performance (Brotons et al., 2004). However, absence records
are often not available and may be unreliable in some cases. In particular,
absences may be recorded when the species was not detected even though the
environment was suitable. These cases are often referred to as ‘false absences’
because the model will interpret the record as denoting unsuitable environmental
conditions, even though this is not the case. False absences can occur when a
species could not be detected although it was present, or when the species was
absent but the environment was in fact suitable (e.g. due to dispersal limitation,
or metapopulation dynamics). Inclusion of false absence records may seriously
bias analyses, so absence data should be used with care (Hirzel et al., 2002).
There are a number of additional potential sources of bias and error that should
be carefully considered when collating species’ distribution data. Errors may
arise through the incorrect identification of species, or inaccurate spatial
referencing of samples. Biases can also be introduced because collectors tend to
sample in easily accessible locations, such as along roads and rivers and near
towns or biological stations (Graham et al., 2004a). In some cases, biased
sampling in geographical space may lead to non-representative sampling of the
available environmental conditions, although this is not necessarily the case.
When utilizing records from museum collections, it should be remembered that
these data were not generally collected with the purpose of determining the
distributional limits of a species; rather, sampling for museum collections tends to
be biased toward rare and previously unknown species.
20
Environmental data
A wide range of environmental input variables have been employed in species’
distribution modeling. Most common are variables relating to climate (e.g.
temperature, precipitation), topography (e.g., elevation, aspect), soil type and
land cover type (see Table 2). Variables tend to describe primarily the abiotic
environment, although there is potential to include biotic interactions within the
modeling. For example, Heikkinen et al. (2007) used the distribution of
woodpecker species to predict owl distributions in Finland since woodpeckers
excavate cavities in trees that provide nesting sites for owls.
As noted in Section 1, variables are often processed to generate new variables
that are thought to have a direct physiological or behavioral role in determining
species’ distributions. In general, it is advisable to avoid predictor variables that
have an indirect influence on species’ distributions, since indirect associations
may cause erroneous predictions when models are used to predict the species’
distribution in new regions or under alternative climate scenarios (Guisan and
Thuiller, 2005). For example, species do not respond directly to elevation, but
rather to changes in temperature and air pressure that are affected by elevation.
Thus, a species characterized as living at high elevation in a low latitude region
may, in fact, be associated with lower elevations in areas with higher latitude,
since the regional climate is cooler.
Environmental variables may comprise either continuous data (data that can take
any value within a certain range, such as temperature or precipitation) or
categorical data (data that are split into discrete categories, such as land cover
type or soil type). Categorical data cannot be used with a number of common
modeling algorithms (see Section 4). In these cases, it may be possible to
generate a continuous variable from the categorical data. For example, Pearson
et al. (2002) estimated soil water holding capacity from categorical soil data, and
used these values within a water balance model to generate continuous
predictions of soil moisture surplus and deficit.
Modern technologies, including remote sensing (see NCEP module Applications
of remote sensing to ecological modeling), the internet, and GIS have greatly
facilitated the collection and dissemination of environmental datasets (see Table
2). In addition, global climate models have been used to generate scenarios of
future climates and to simulate climatic conditions since the end of the last glacial
period (see Table 2). Predicted future climate scenarios can be used to estimate
the potential impacts of climate change on biodiversity (e.g. Thomas et al. 2004;
see case study 3), whilst simulations of past climates can be used to test the
predictive ability of models (e.g. Martinez-Meyer et al., 2004). Given the vast
amounts of data that are available, it is especially important to remain critical as
to which variables are suitable for inclusion in the model. Some studies have
demonstrated good predictive ability using only three variables (e.g., Huntley et
al., 1995), whilst other studies have applied methodologies that can incorporate
many more variables (e.g., Phillips et al., 2006 utilized 14 environmental
21
variables, although some of these variables are likely to have been rejected by
the algorithm applied because they did not provide useful information beyond
that which was included in other variables).
4. MODELING ALGORITHMS
A number of alternative modeling algorithms have been applied to classify the
probability of species’ presence (and absence) as a function of a set of
environmental variables. The task is to identify potentially complex non-linear
relationships in multi-dimensional environmental space. In Section 2 we assumed
that the modeling algorithm is excellent, enabling us to identify three expected
types of model prediction, illustrated by modeled areas 1, 2 and 3 in Fig. 3. If we
now admit some degree of error in the algorithm’s ability to fit the observed
records, then a fourth type of prediction will occur: the model will predict as
suitable areas that are part of neither the actual nor the potential distribution. The
most useful algorithms will limit these erroneous ‘type 4’ predictions.
Table 3 lists some commonly used approaches for species’ distribution modeling.
Some methods that have been applied are statistical (e.g. generalized linear
models [GLMs] and generalized additive models [GAMs]), whilst other
approaches are based on machine-learning techniques (e.g., maximum entropy
[Maxent] and artificial neural networks [ANNs]). Published studies have often
applied one or more of these algorithms and have given the resulting model a
name or acronym (e.g., ‘Maxent’ refers to an implementation of the maximum
entropy method, whilst ‘BIOMOD’ is the acronym given to a model that
implements a number of methods, including GLMs and GAMs). Often these
models have been implemented in user-friendly software that is free and easy to
obtain (Table 3).
22
Table 3. Some published methods for species’ distribution modeling.
Method(s)1
Model/software name2
Species data type
Gower Metric
DOMAIN*
presence-only
Ecological Niche Factor
Analysis (ENFA)
Maximum Entropy
BIOMAPPER*
presence and background
MAXENT*
presence and background
Genetic algorithm (GA)
GARP *
pseudo-absence
SPECIES
presence and absence
(or pseudo-absence)
presence and absence
(or pseudo-absence)
Artificial Neural Network
(ANN)
Regression:
generalized linear model
(GLM), generalized
additive model (GAM),
boosted regression trees
(BRT), multivariate
adaptive regression
splines (MARS)
Multiple methods
Multiple methods
1
3
4
5
Implemented in R
BIOMOD
OpenModeller
presence and absence
(or pseudo-absence)
depends on method
implemented
Key reference/URL
Carpenter et al. 1993
http://www.cifor.cgiar.org/docs/_ref/research_tools/dom
ain/
http://diva-gis.org
Hirzel et al. 2002
http://www2.unil.ch/biomapper/
Phillips et al. 2006
http://www.cs.princeton.edu/~schapire/maxent/
Stockwell and Peters 1999
http://www.lifemapper.org/desktopgarp/
Pearson et al. 2002
Lehman et al. 2002
Elith et al. 2006
Leathwick et al. 2006
Elith et al. 2007
Thuiller 2003
http://openmodeller.sourceforge.net/
2
‘Method’ refers to a statistical or machine-learning technique. ‘Model/software name’ refers to a name (or acronym) given to a published model
that implements the method(s) stated. Software to implement the method for species’ distribution modeling is readily available at no cost for those
3
models marked with an asterisk (*); other models are available at the discretion of the author(s). The genetic algorithm for rule-set prediction
4
(GARP) includes within its processing multiple methods, including GLM. Note that Pseudo-absence here refers to the sampling approach
5
implemented in the GARP software; in principle, any presence-absence method can be implemented using pseudo absences. R is a freely
available (at no cost) software environment for statistical computing and graphics (http://www.r-project.org/).
Based in part on Elith et al. (2006) and Guisan and Thuiller (2005).
23
There are some important differences between among model algorithms that
should be carefully considered when selecting which method(s) to apply. One
key factor is whether the algorithm requires data on observed species absence
(Section 3). Some algorithms operate by contrasting sites where the species has
been detected with sites where the species has been recorded as absent (e.g.,
GLMs, GAMs, ANNs). However, reliable absence data often are not available
(Section 3), so other methods have been applied that do not require absence
data. We can distinguish three types of presence-only methods:
1) Methods that rely solely on presence records (e.g. BIOCLIM, DOMAIN).
These methods are truly ‘presence-only’ since the prediction is made
without any reference to other samples from the study area.
2) Methods that use ‘background’ environmental data for the entire study
area (e.g. Maxent, ENFA). These methods focus on how the environment
where the species is known to occur relates to the environment across the
rest of the study area (the ‘background’). An important point is that the
occurrence localities are also included as part of the background.
3) Methods that sample ‘pseudo-absences’ from the study area. In principle,
any presence/absence algorithm can be implemented using pseudoabsences. The aim here is to assess differences between the occurrence
localities and a set of localities chosen from the study area that are used
in place of real absence data. The set of ‘pseudo-absences’ may be
selected randomly (e.g., Stockwell and Peters, 1999) or according to a set
of weighting criteria (e.g., Engler et al., 2004; Zaniewski et al., 2002). An
important difference between the pseudo-absence approach and the
background approach is that pseudo-absence models do not include
occurrence localities within the set of pseudo-absences.
Another key difference among model algorithms is their ability to incorporate
categorical environmental variables (see Section 3). Methods also differ in the
form of their output, which is most commonly a continuous prediction (e.g. a
probability value ranging from 0 to 1) but may be a binary prediction (with ‘0’ as a
prediction of unsuitable environmental conditions or species absence, and ‘1’ a
prediction of highly suitable environmental conditions or species presence). To
generate a binary prediction from a model that gives continuous output, it is
necessary to set a threshold value above which the prediction is classified as
‘highly suitable’ or ‘present’ (see Section 5).
A further consideration when selecting a modeling algorithm is whether it is
important to determine the relative influence of different input variables on the
model’s fit or predictive capacity. Some models may have excellent predictive
power but do not enable us to easily understand how the algorithm is operating;
such models are often termed ‘black box’ since the model takes input and
produces output but the internal workings are somewhat opaque. For example,
artificial neural networks have shown good predictive ability (e.g., Pearson et al.,
2002; Segurado and Araújo, 2004; Thuiller, 2003), but identifying the relative
24
contribution of each input variable to the prediction is difficult (sensitivity analysis
may be used, but this requires additional analyses). In contrast, a GLM builds a
regression equation from which the relative contributions of different variables
are immediately apparent (Guisan et al., 2002).
It is not possible within the scope of this synthesis to describe the theory,
advantages and disadvantages of a large number of modeling algorithms; the
reader is referred to the literature cited in Table 3. However, see Box 3 and the
practical exercise by Steven Phillips that accompanies this Synthesis for a more
detailed description of one method, Maxent.
25
Box 3. Maximum Entropy (Maxent) modeling of species distributions
(based on Phillips et al., 2006)
Maxent is a general-purpose method for characterizing probability
distributions from incomplete information. In estimating the probability
distribution defining a species’ distribution across a study area, Maxent
formalizes the principle that the estimated distribution must agree with
everything that is known (or inferred from the environmental conditions
where the species has been observed) but should avoid making any
assumptions that are not supported by the data. The approach is thus to
find the probability distribution of maximum entropy (the distribution that is
most spread-out, or closest to uniform) subject to constraints imposed by
the information available regarding the observed distribution of the species
and environmental conditions across the study area.
The Maxent method does not require absence data for the species
being modeled; instead it uses background environmental data for the
entire study area. The method can utilize both continuous and categorical
variables and the output is a continuous prediction (either a raw probability
or, more commonly, a cumulative probability ranging from 0 to 100 that
indicates relative suitability). Maxent has been shown to perform well in
comparison with alternative methods (Elith et al., 2006; Pearson et al.,
2007; Phillips et al., 2006). One drawback of the Maxent approach is that
it uses an exponential model that can predict high suitability for
environmental conditions that are outside the range present in the study
area (i.e. extrapolation, see Box 1). To alleviate this problem, when
predicting for variable values that are outside the range found in the study
area, these values are reset (or ‘clamped’) to match the upper or lower
values found in the study area.
For a concise mathematic definition of Maxent and for more detailed
discussion of its application to species distribution modeling see Phillips et
al. (2004, 2006). These authors have developed software with a userfriendly interface to implement the Maxent method for modeling species
distributions (for free download see web link in Table 3). The software also
calculates a number of alternative thresholds (see Section 5), computes
model validation statistics (see Section 5), and enables the user to run a
jackknife procedure to determine which environmental variables contribute
most to the model prediction (see the practical exercise by Steven Phillips
that accompanies this synthesis).
The model algorithm is in some ways the ‘core’ of the distribution model, but it
should be remembered that the algorithm is just one part of the broader modeling
process; other factors, including selection of environmental variables (Section 3)
and application of a decision threshold (Section 5), are key elements of the
modeling process that affect model results and may be varied regardless of the
model algorithm being used. Nevertheless, studies comparing different modeling
algorithms have demonstrated substantial differences between predictions from
26
alternative methods. The importance of selecting an appropriate algorithm is
discussed below.
Differences between methods and selection of ‘best’ models
Given the variety of possible modeling methods (Table 3), it is important to
consider the degree to which different methods yield different results.
Furthermore, if model predictions differ substantially, how should we choose
which method to apply? This is an active area of research, and unfortunately
there are no simple answers.
A number of studies have demonstrated that different modeling approaches have
the potential to yield substantially different predictions (e.g., Brotons et al., 2004;
Elith et al., 2006; Loiselle et al., 2003; Pearson et al., 2006; Segurado and
Araújo, 2004; Thuiller, 2003; Thuiller et al., 2004). Pearson et al. (2006) found
especially large differences among predictions of changes in range size under
future climate change scenarios based on nine alternative modeling methods.
Predicted changes in range size differed in both magnitude and direction (e.g.
from 92% range reduction to 322% range increase for a single species). In
another study, Loiselle et al. (2003) demonstrated markedly different results
when alternative distribution models were used alongside a reserve selection
algorithm for identifying priority sites for conservation.
The most comprehensive model comparison to date was provided by Elith et al.
(2006). The authors compared 16 modeling methods using 226 species across
six regions of the world. All of the models included in the study were
implemented using presence-only data for calibration (some methods required
the use of pseudo-absence data), but model performance was assessed using
data on both presence and absence. These analyses found differences between
predictions from alternative methods, but also found that some methods
consistently outperformed others. In general, models classified as ‘best’ were
those that were able to identify complex relationships that existed in the data,
including interactions among environmental variables.
Several additional factors that lead to differences among predictions from
alternative algorithms have been identified. These include (1) whether the model
uses presence-absence or presence-only data (Brotons et al., 2004; Pearson et
al., 2006), (2) if the model does not use absence data, whether the model uses
solely presence records, ‘background’ data, or ‘pseudo-absences’ (Elith et al.,
2006), (3) whether the algorithm is parametric or non-parametric (Segurado and
Araújo, 2004), and (4) how the model ‘extrapolates’ beyond the range of data
used for its calibration (Pearson et al., 2006; and see Box 1).
In view of these differences among models, selection of an appropriate algorithm
is both difficult and crucial. Identifying models that are generically ‘best’ is
problematic since the approach used to assess predictive performance depends
on the aim of the modeling. For example, Elith et al. (2006) assessed the ability
27
of models to simulate actual distributions by using statistical tests that reward
models for correctly classifying both presences and absences (see Section 5). In
contrast, Pearson et al. (2007) assessed predictive performance based only on
the model’s ability to predict observed presences, arguing that the purpose of the
modeling was to identify potential distributions (in which case use of absence
data in assessing performance is invalid since a site classified as absent still may
be environmentally suitable). The relative merits of aiming to predict actual
versus potential distributions were discussed in Section 2. We will also return to
the question of how to identify ‘best’ models when describing various statistical
approaches for assessing predictive performance in Section 5. However, the
important point is that it is not straightforward to identify which methods are best,
and it is therefore not possible to recommend use of one method over another.
In practice, model selection will be influenced by factors including whether
observed absence data are available, whether data on some of the
environmental variables are categorical, and whether it is important to evaluate
the influence of different variables on the model prediction. We recommend that
modeling efforts apply and examine predictions from a range of methods in order
to quantify uncertainty arising from the choice of method and to identify when
different models are in agreement. Perhaps most importantly, it is vital that the
assumptions and behavior of any model are properly understood (e.g. how does
the model deal with environmental conditions that are beyond the range of the
data used to calibrate the model?) so that model output can be accurately
interpreted.
5. ASSESSING PREDICTIVE PERFORMANCE
Assessing the accuracy of a model’s predictions is commonly termed ‘validation’
or ‘evaluation’, and is a vital step in model development. Application of the model
will have little merit if we have not assessed the accuracy of its predictions.
Validation thus enables us to determine the suitability of a model for a specific
application and to compare different modeling methods (Pearce and Ferrier,
2000). This section discusses different approaches for assessing predictive
performance, including strategies for obtaining data against which the predictions
can be compared, methods for selecting thresholds of occurrence, and various
test statistics. As in previous sections, there is no single approach that can be
recommended for use in all modeling exercises; rather, the choice of validation
strategy will be influenced by the aim of the modeling effort, the types of data
available, and the modeling method used.
Strategies for obtaining test data
In order to test predictive performance it is necessary to have data against which
the model predictions can be compared. We can refer to these as test data
(sometimes called evaluation data) to distinguish them from the calibration data
(sometimes called training data) that are used to build the model. It is fairly
common for studies to assess predictive performance by simply testing the ability
28
of the model to predict the calibration data (i.e. calibration and test datasets are
identical). However, this approach makes it difficult to identify models that have
over-fit the calibration data (meaning the model is able to accurately classify the
calibration data, but the model performs poorly when predicting test data),
making it impossible for users to judge how well the model may perform when
making predictions (Araújo et al., 2005a). It is therefore preferable to use test
data that are different from the calibration data.
Ideally, test data would be collected independently from the data used to
calibrate the model. For example, Fleishman et al. (2002) modeled the
occurrence of butterfly species in Nevada, USA, using species inventory data
collected during the period 1996-1999, and then tested the models using data
collected from new sites during 2000-2001 (see Case Study 1 for a comparable
study). Other researchers have undertaken validation using independent data
from different regions (e.g. Beerling et al., 1995; Peterson, 2003), data at
different spatial resolution (e.g., Araújo et al., 2005b; Pearson et al., 2004), data
from different time periods (e.g., Araújo et al., 2005a), and data from surveys
conducted by other researchers (Elith et al., 2006).
However, in practice it may not be possible to obtain independent test data and it
is therefore common to partition the available data into calibration and test
datasets. Several strategies are available for partitioning data, the simplest being
a one-time split in which the available data are assigned to calibration and test
datasets either randomly (e.g., Pearson et al., 2002) or by dividing the data
spatially (e.g., Peterson and Shaw, 2003). The relative proportions of data
included in each data set are somewhat arbitrary, and dependent on the total
number of locality points available (though using 70% for calibration and 30% for
testing is common, following guidelines provided by Huberty (1994)). An
alternative to a one-time split is ‘bootstrapping’, whereby the data are split
multiple times. Bootstrapping methods sample the original set of data randomly
with replacement (i.e. the same occurrence record could be included in the test
data more than once). Multiple models are thus built, and in each case predictive
performance is assessed against the corresponding test data. Validation
statistics can then be reported as the mean and range from the set of bootstrap
samples (e.g., Buckland and Elston, 1993; Verbyla and Litaitis, 1989). An
approach similar to bootstrapping, but sampling without replacement (i.e. the
same occurrence record cannot be included in the test data more than once),
can also be applied and may be termed ‘randomization’ (Fielding and Bell, 1997).
Another useful data partitioning method is k-fold partitioning. Here, data are split
into k parts of roughly equal size (k > 2) and each part is used as a test set with
the other k-1 sets used for model calibration. Thus, if we select k = 5 then five
models will be calibrated and each model tested against the excluded test data.
Validation statistics are then reported as the mean and range from the set of k
tests (Fielding and Bell, 1997). An extreme form of k-fold partitioning, with k
equal to the number of occurrence localities, is recommended for use with very
29
low sample sizes (e.g., < 20; Pearson et al., 2007). This method is termed
‘jackknifing’ or ‘leave-one-out’ since each occurrence locality is excluded from
model calibration during one partition.
The following sub-sections describe validation statistics that can be calculated
after test data have been obtained using one of the above approaches.
The presence/absence confusion matrix
If a model is used to predict a set of test data, predictive performance can be
summarized in a confusion matrix. Note that binary model predictions (i.e.
predictions of suitable and unsuitable, rather than probabilities; see section 4) are
required in order to complete the confusion matrix. Later subsections describe
methods for converting continuous model outputs into binary predictions (see
Selecting thresholds of occurrence) and for assessing predictive performance
using continuous predictions (see Threshold-independent assessment).
However, in order to understand these later sections it is important to first look at
the confusion matrix.
The confusion matrix is rather more straightforward than its name suggests, and
is alternatively termed an ‘error matrix’ or a ‘contingency table’. The confusion
matrix records the frequencies of each of the four possible types of prediction
from analysis of test data: (a) true positive (the model predicts that the species is
present and test data confirms this to be true), (b) false positive (the model
predicts presence but test data show absence), (c) false negative (the model
predicts absence but test data show presence), (d) true negative (the model
predicts and the test data show absence). Frequencies are commonly recorded
in a confusion matrix with the following form:
predicted
present
predicted
absent
recorded present
recorded absent
a (true positive)
b (false positive)
c (false negative)
d (true negative)
Each element of the confusion matrix can be visualized in geographical space as
illustrated in Figure 4. In the example depicted, 27 test localities have been
sampled and presence or absence of the species recorded at each site. The use
of test data comprising only presence localities (i.e. species occurrence records)
is discussed below, but for completion of the confusion matrix we require both
presence and absence records. Thus, the hypothetical case shown in Figure 4
would yield the following confusion matrix:
30
predicted
present
predicted
absent
recorded present
recorded absent
9
2
3
13
The frequencies in the confusion matrix form the basis for a variety of different
statistical tests that can be used to assess model performance. Most of the
commonly used tests are described below. Terminology related to model
performance often varies from study to study and is sometimes not intuitive. In
particular, false negative predictions are commonly termed errors of ‘omission’,
whilst false positive predictions are termed errors of ‘commission’.
Figure 4. Diagram illustrating the four types of outcomes that are possible when assessing the
predictive performance of a species distribution model: true positive, false positive, false negative
and true negative. The diagram uses the same hypothetical actual and modeled distributions as
in Figure 3. Each instance of a symbol (x, □, ○, -) on the map depicts a site that has been
surveyed and presence or absence of the species recorded (it is assumed here that if a site falls
within the actual distribution then the species will be detected). These survey records constitute
the test data. Frequencies of each type of outcome are commonly entered into a confusion matrix
(see main text).
31
Test statistics derived from the confusion matrix
A simple measure of predictive performance that can be derived from the
confusion matrix is the proportion (or percentage) of test localities that are
correctly predicted, calculated as
( a + d ) /( a + b + c + d )
This measure may be termed ‘accuracy’ or ‘correct classification rate’. The
concept of accuracy is simple and logical, but it is possible to obtain high
accuracy using a poor model when a species’ prevalence (the proportion of
sampled sites in which the species is recorded present) is relatively high or low.
For example, if prevalence is 5% then 95% of test localities can be correctly
classified simply by predicting all sites as ‘absent’. To circumvent this problem,
Cohen (1960) introduced a measure of accuracy that is adjusted to account for
chance agreement between predicted and observed values. The statistic, Kappa
(k), is similar to accuracy but the proportion of correct predictions expected by
chance is taken into account (for full derivation see Monserud and Leemans,
1992). Kappa is calculated as
[(a + d ) − ((( a + c)(a + b) + (b + d )(c + d )) / n)]
[n − (((a + c)(a + b) + (b + d )(c + d )) / n)]
Accuracy and Kappa statistics use all values in the confusion matrix and
therefore require both presence and absence data. However, absence data are
often unavailable (e.g. when using specimens from museum collections) and are
inappropriate for use when the aim is to estimate the potential distribution (since
the environment may be suitable even though the species is absent).
When only presence records are used, the proportion of observed occurrences
correctly predicted can be calculated as
a /( a + c )
This measure is sometimes termed ‘sensitivity’ or ‘true positive fraction’.
Alternatively, we may calculate
c /( a + c )
which is often termed ‘omission rate’ or ‘false positive fraction’. Note that these
two measures – sensitivity and omission rate – sum to 1. Thus, high sensitivity
means low omission, and low sensitivity means high omission. Although
sensitivity and omission rate avoid the use of absence records, a serious
disadvantage of these tests is that it is possible to achieve very high sensitivity
(and low omission) simply by predicting that the species is present at an
32
excessively large proportion of the study area. In short, it is possible to cheat: if
the model predicts the entire study area to be suitable, then sensitivity will equal
1, and omission rate will be zero. To avoid this problem, it is necessary to test the
statistical significance of a sensitivity or omission rate score.
To test for statistical significance, we ask whether the accuracy of our predictions
is greater than would be expected by chance. Imagine, for example, that we are
blindfolded and asked to throw darts at a map of our study area. The sites
identified by our random throws are then used as species’ occurrence localities
for model testing. The probability of landing darts in the area predicted by the
model to be suitable for the species is equal to the proportion of the study area
that is predicted as suitable. Thus, if the model predicts that the species will be
present in 40% of the study area, then our probability of successfully landing a
dart in the area predicted as suitable is 0.4.
We can apply the same logic to assess the statistical significance of a sensitivity
(or omission rate) score. In this case, we use an exact one-tailed binomial test (or
for larger sample sizes a chi-square test; for description of binomial and chisquare tests see Zar, 1996) to calculate the probability of obtaining a sensitivity
result by chance alone (Anderson et al., 2002a). For example, suppose that the
model in Figure 4 predicts that 30% of the study area is suitable for the species.
The probability of success by chance alone for each test locality is therefore 0.3.
We can calculate from the confusion matrix that the sensitivity = 9/(9+3) = 0.75,
and we can use an exact one-tailed binomial test to calculate that the probability
of making nine or more successful predictions of presence by chance alone is
0.0017. We may therefore conclude that our result is statistically significant (p <
0.01).
A similar assessment of predictive performance can be conducted when only
very few occurrence localities are available and test data have been generated
using a jackknifing approach (see subsection Strategies for obtaining test data).
In this case the number of successful predictions from a set of jackknife trials can
be calculated (e.g., 9 successes in 12 jackknife trials) and a p-value can be
calculated using the method presented in Pearson et al. (2007).
In practice, binomial and chi-square tests can be performed in most standard
statistical packages, whilst the jackknife p-value can be calculated using software
provided as Supplementary Material to the Pearson et al. (2007) paper. Various
test statistics and thresholds (including those discussed in the remainder of this
section) are sometimes calculated automatically by software designed for
species distribution modeling (see Table 3), and test statistics may also be
calculated using more general applications such as DIVA-GIS (for free download
see http://www.diva-gis.org/).
33
Another statistic that can be derived from the confusion matrix is the proportion of
observed absences that are correctly predicted, calculated as
d /(b + d )
This statistic is commonly termed ‘specificity’ or ‘true negative fraction’.
Specificity is rarely used as a test statistic on its own, since specificity focuses
solely on observed absence records. However, specificity is an important
measure used in setting decision thresholds and in ROC analysis, which are
described in the following two subsections.
Selecting thresholds of occurrence
Binary predictions of ‘present’ or ‘absent’ are necessary to test model
performance using statistics derived from the confusion matrix. It is therefore
often useful to convert continuous model output into binary predictions by setting
a threshold probability value above which the species is predicted to be present.
Although an alternative test statistic that does not require a threshold is available
(Area Under the ROC curve; see the following subsection), this approach is not
suitable in many circumstances (notably when absence records are not available,
Boyce et al., 2002, but see Phillips et al., 2006). Furthermore, it is essential to
learn the techniques described in this subsection to understand how the AUC
test operates.
A number of different methods have been employed for selecting thresholds of
occurrence (Table 4). Perhaps the simplest approach is to use an arbitrary value,
but this method is subjective and lacks ecological reasoning (Liu et al., 2005).
Other methods use criteria that are based on the data used to calibrate the
model. One approach is to use the lowest predicted value of environmental
suitability, or probability of presence, across the set of sites at which a species
has been detected. This method assumes that species presence is restricted to
locations equally or more suitable than those at which the species has been
observed. The approach therefore identifies the minimum area in which the
species occurs whilst ensuring that no localities at which the species has been
observed are omitted (i.e. omission rate = 0, and sensitivity = 1). An alternative
approach is to set the threshold to allow a certain amount of omission (e.g. 5%),
which is analogous to setting a fixed sensitivity (e.g. 0.95). This method is less
sensitive than the lowest predicted value method to ‘outliers’ (i.e. locations in
which the species is detected despite a low predicted probability of occurrence or
suitability), but errors of omission are imposed (i.e. some observed localities will
be omitted from the prediction).
34
Table 4. Some published methods for setting thresholds of occurrence.
Method
Fixed value
Lowest predicted value
Fixed sensitivity
Sensitivity-specificity equality
Sensitivity-specificity sum
maximization
Maximize Kappa
Average probability/suitability
Equal prevalence
Definition
An arbitrary fixed value (e.g. probability = 0.5)
The lowest predicted value corresponding with
an observed occurrence record
The threshold at which an arbitrary fixed
sensitivity is reached (e.g. 0.95, meaning
that 95% of observed localities will be
included in the prediction)
The threshold at which sensitivity and specificity
are equal
The sum of sensitivity and specificity is
maximized
The threshold at which Cohen’s Kappa statistic
is maximized
The mean value across model output
Species’ prevalence (the proportion of
presences relative to the number of sites)
is maintained the same in the prediction as
in the calibration data.
Species data type1
presence-only
presence-only
presence-only
presence and
absence
presence and
absence
presence and
absence
presence-only
presence and
absence
Reference(s)
Manel et al. 1999,
Robertson et al. 2001
Pearson et al. 2006,
Phillips et al. 2006
Pearson et al. 2004
Pearson et al. 2004
Manel et al. 2001
Huntley et al. 1995,
Elith et al. 2006
Cramer 2003
Cramer 2003
1
Species occurrence records required to set the threshold.
Based in part on Liu et al. (2005).
35
Many methods for setting thresholds can be implemented by calculating statistics
derived from the confusion matrix across the range of possible thresholds. For
example, sensitivity and specificity may be calculated at thresholds increasing in
increments of 0.01 from 0 to 1 (i.e. 0, 0.01, 0.02, 0.03…0.99, 1). As the threshold
increases, the proportion of the study area predicted to be suitable for the
species, or in which the species is predicted to be ‘present,’ will decrease.
Consequently, the proportion of observed presences that are correctly predicted
decreases (i.e. decreasing sensitivity) and the proportion of observed absences
that are correctly predicted increases (i.e. increasing specificity) (Figure 5A).
From these data we can select the threshold at which sensitivity and specificity
are equal (labeled a in Figure 5A) or at which their sum is maximized. Similarly, it
is common to calculate Kappa across the range of possible thresholds and to
select the threshold at which the statistic is maximized (Figure 5B).
Figure 5. Plots showing changes in test statistics as the threshold of occurrence is adjusted. A.
Decrease in sensitivity and increase in specificity as the threshold is increased. The threshold
labeled a corresponds to the specificity-sensitivity equality threshold. B. Changes in the Kappa
statistic as the threshold is adjusted. The threshold labeled b corresponds to that threshold at
which Kappa is maximized.
Choice of an appropriate decision threshold is dependent on the type of data that
are available and the question that is being addressed. Some methods require
presence and absence records, whilst others require presence-only records
(Table 4). When using both presence and absence records, the general
approach is to balance the number of observed presences and absences that are
correctly predicted; in effect, to maximize agreement between observed and
predicted distributions. Thus, we must be willing to increase the omission rate
(i.e. decrease sensitivity) in order to increase the proportion of observed
absences that are correctly predicted (i.e. increase specificity). Liu et al. (2005)
tested twelve methods for setting thresholds using presence and absence data
for two European plant species. Based on four assessments of predictive
performance (sensitivity, specificity, accuracy and Kappa), they concluded that
36
the best methods for setting thresholds included maximizing the sum of
sensitivity and specificity, using the average probability/suitability score, and
setting equal prevalence between the calibration data and the prediction (Table
4). Maximizing Kappa did not perform well, and use of an arbitrary fixed value
performed worst.
Methods that use only presence records for setting a threshold are required for
cases in which absence data are unavailable. Presence-only methods can also
be justified on the grounds that they avoid false absences (Section 3): it may be
argued that we should be primarily concerned with maximizing the number of
observed presences that are correctly predicted, rather than minimizing the
number of absences that are incorrectly predicted as presences (since some
absences may be recorded in apparently suitable environments; Pearson et al.,
2006). For example, Pearson et al. (2007) used a dataset comprising very few
presence-only records for geckos in Madagascar. Because confidence was high
that the localities and species identification were correct, and because these
species are not highly mobile and are therefore unlikely to be found in unsuitable
habitat (i.e. sink habitat; see section 2), omission of any occurrence record was
considered a clear model error. Therefore, the minimum predicted value
corresponding to an observed presence was selected as a threshold to ensure
zero omission. Distribution models thus predicted that many regions of the study
area were suitable although no presences had been detected there. This
approach suited the aim of the study, which was to prioritize regions for future
surveys by estimating the potential distribution (see Case Study 1).
As a final illustration of the importance of selecting an appropriate decision
threshold, we can return to an example raised in Section 2. If the purpose of
modeling is to identify areas within which disturbance may impact a species
negatively (e.g. as part of an environmental impact assessment), then the
threshold may be set low to identify a larger area of potentially suitable habitat. In
contrast, if the model was intended to identify potential introduction or
reintroduction sites for an endangered species or species of recreational value,
then it would be appropriate to choose a relatively high threshold. Choosing a
high threshold reduces the risk of choosing unsuitable sites by identifying those
areas with highest suitability (Pearce and Ferrier, 2000).
Threshold-independent assessment
When model output is continuous, assessment of predictive performance using
statistics derived from the confusion matrix will be sensitive to the method used
to select a threshold for creating a binary prediction. Furthermore, if predictions
are binary, the assessment of performance does not take into account all of the
information provided by the model (Fielding and Bell, 1997). Therefore, it is often
useful to derive a test statistic that provides a single measure of predictive
performance across the full range of possible thresholds. This can be achieved
using a statistic known as AUC: the Area Under the Receiver Operating
Characteristic Curve.
37
The AUC test is derived from the Receiver Operating Characteristic (ROC)
Curve. The ROC curve is defined by plotting sensitivity against ‘1 – specificity’
across the range of possible thresholds (Figure 6A). Sensitivity and specificity
are used because these two measures take into account all four elements of the
confusion matrix (true and false presences and absences). It is conventional to
subtract specificity from 1 (i.e. 1 – specificity) so that both sensitivity and
specificity vary in the same direction when the decision threshold is adjusted
(Pearce and Ferrier, 2000). The ROC curve thus describes the relationship
between the proportion of observed presences correctly predicted (sensitivity)
and the proportion of observed absences incorrectly predicted (1 – specificity).
Therefore, a model that predicts perfectly will generate an ROC curve that
follows the left axis and top of the plot, whilst a model with predictions that are no
better than random (i.e. is unable to classify accurately sites at which the species
is present and absent) will generate a ROC curve that follows the 1:1 line (Figure
6A).
Figure 6. Example Receiver Operating Characteristic (ROC) Curves and illustrative frequency
distributions. A. ROC curves formed by plotting sensitivity against ‘1 – specificity’. Two ROC
curves are shown, the upper curve (red) signifying superior predictive ability. The dashed 1:1 line
signifies random predictive ability, whereby there is no ability to distinguish occupied and
unoccupied sites. B and C show example frequency distributions of probabilities predicted by a
model for observed ‘presences’ and ‘absences’. The results shown in B reveal good ability to
distinguish presence from absence, whilst results in C show more overlap between the frequency
distributions thus revealing poorer classification ability. The case shown in B would produce an
ROC curve similar to the upper (red) curve in A. The case shown in C would give an ROC curve
more like the lower (blue) curve in A.
In order to summarize predictive performance across the full range of thresholds
we can measure the area under the ROC curve (the AUC), expressed as a
proportion of the total area of the square defined by the axes (Swets, 1988). The
38
AUC thus ranges from 0.5 for models that are no better than random to 1.0 for
models with perfect predictive ability. We can think of AUC in terms of the
frequency distributions of probabilities predicted for locations at which we have
empirical data on presence and absence (Figure 6, B and C). A high AUC score
reflects that the model can discriminate accurately between locations at which
the species is present or absent. In fact, AUC can be interpreted as the
probability that a model will correctly distinguish between a presence record and
an absence record if each record is selected randomly from the set of presences
and absences. Thus, an AUC value of 0.8 means the probability is 0.8 that a
record selected at random from the set of presences will have a predicted value
greater than a record selected at random from the set of absences (Fielding and
Bell, 1997; Pearce and Ferrier, 2000).
AUC is a test that uses both presence and absence records. However, Phillips et
al. (2006) have demonstrated how the test can be applied using randomly
selected ‘pseudo-absence’ records in lieu of observed absences. In this case,
AUC tests whether the model classifies presence more accurately than a random
prediction, rather than whether the model is able to accurately distinguish
presence from absence.
A number of different methods can be used to compute the AUC (Pearce and
Ferrier, 2000). Some distribution modeling programs automatically calculate the
AUC (e.g. Maxent; Table 3). The statistic can also be calculated using numerous
other free software packages (e.g. R, for free download see http://www.rproject.org/).
Choosing a suitable test statistic
The choice of test statistic depends largely on how the model will be applied. If
the aim is to predict the actual distribution (Section 2) then use of a test that
incorporates both presence and absence records may be preferable (e.g.
accuracy or Kappa). A good model will successfully predict both presences and
absences with equal frequency. However, when using this approach it is
important to realize that predictions that an unoccupied area is environmentally
suitable (type 3 predictions, Figure 3) are considered model errors. Because type
3 predictions are theoretically expected (Section 2), models may be judged poor
although they make biologically sound predictions.
If the aim of the modeling is to estimate the potential distribution (Section 2) then
presence-only assessment of model performance using sensitivity and statistical
significance is likely to be preferable. In this case we cannot test if the model is
correct (since we do not know the true potential distribution), but rather we test if
the model is useful. Our criteria for usefulness are that the model successfully
predicts presence in a high proportion of test localities (i.e., known occurrences)
whilst not predicting that an excessively large proportion of the study area is
suitable. Thus, a model that successfully predicts whether the species is present
at all test localities whilst classifying most of the study area as suitable may be
39
correct (the environment may truly be suitable throughout most of the study
area); however, the model is not useful because it is not more informative than a
random prediction.
Subjective guidelines can be used to decide what values of a test statistic
correspond to ‘good’ model performance. For example, Landis and Koch (1977)
suggested that Kappa scores >0.75 represent an ‘excellent’ model, whilst Swets
(1988) classified any AUC score >0.9 as ‘very good’. However, the only true test
of the model is whether it is useful for a given application. There are numerous
potential applications of these methods (Table 1) and the final part of this
synthesis describes three representative case studies.
PART C: CASE STUDIES
CASE STUDY 1: PREDICTING DISTRIBUTIONS OF KNOWN AND UNKNOWN
SPECIES IN MADAGASCAR (BASED ON RAXWORTHY ET AL., 2003)
Our knowledge of the identity and distribution of species on Earth is remarkably
poor, with many species yet to be described and catalogued. This problem has
two key elements, which may be termed the ‘Linnean’ and ‘Wallacean’ shortfalls
(Whittaker et al., 2005). The Linnean shortfall refers to our lack of knowledge of
how many, and what kind, of species exist. The term is a reference to Carl
Linnaeus, who laid the foundations of modern taxonomy and the 18th century.
The Linnean shortfall concerns our highly incomplete knowledge of the diversity
of life that exists on Earth.
The Wallacean shortfall refers to our inadequate knowledge of the distributions of
species. This term is a reference to Alfred Russel Wallace who, as well as
contributing to the early development of evolutionary theory, was an expert on
the geographical distribution of species (he is sometimes referred to as ‘the
father of biogeography‘). The Wallacean shortfall thus refers to our poor
knowledge of the biogeography of most species. Species distribution modeling
offers a powerful tool to address both the Linnean and Wallacean shortfalls, as
demonstrated in a study by Raxworthy et al. (2003).
Raxworthy et al. (2003) modeled the distributions of 11 species of chameleon
that are endemic to the island of Madagascar. They used species occurrence
records from recent surveys and from older specimens deposited in collections of
natural history museums. No observed absence records were available for
building the models. Environmental variables were derived from remote sensing
data, from a digital elevation model, and from weather station data that had been
interpolated to a grid (i.e. converted from point vector to raster data). In all, 25
GIS layers were used in the modeling, including environmental variables
describing temperature, precipitation, land cover and elevation. All analyses were
undertaken at a resolution of 1km2. The modeling algorithm used was GARP
(see Table 3), which generated an output ranging from 0 – 10 at increments of 1.
40
Two alternative thresholds of occurrence were used: threshold = 1 (termed by the
authors “any model predicts”), and threshold = 10 (termed “all models predict”).
Predictive performance of the models was first evaluated by splitting the
available data into two parts, 50% for calibrating the model and 50% for testing
the model. The authors calculated the number of test localities at which the
species was correctly predicted to be present and tested the statistical
significance of the results using a chi-square test. Performance of the 11 models
was generally good, with overall prediction success as high as 83%. Predictions
usually were better than random. A second evaluation tested model performance
using independent test data from herpetological surveys undertaken at 11 sites
after the models had been built. In this case, model evaluation was based on
both presence and absence records, since surveys were sufficiently thorough
that detection probability was high. The success of these predictions was more
than 70% and levels of statistical significance were uniformly high.
Raxworthy et al. (2003) thus demonstrated the potential for species’ distribution
models to be used to guide new field surveys toward areas in which the
probability of species presence was high. This approach takes advantage of the
type of model prediction illustrated by area 2 in Figure 3: the model identifies an
area that is environmentally similar to where the species has already been found,
but for which no occurrence data are available. The models can thus help to
address the Wallacean shortfall, by improving our knowledge of the distributions
of known species.
Raxworthy et al. (2003) also demonstrated that the models can help to address
the Linnean shortfall by guiding field surveys toward areas where species new to
science are most likely to be discovered. In this case the approach makes use of
the type of model prediction illustrated by area 3 in Figure 3: areas are identified
that are unoccupied by the species being modeled, but where closely-related
species that occupy similar environmental space are most likely to be found. By
surveying sites identified by the distribution models for known species,
Raxworthy et al. (2003) discovered seven new species, considerably greater
than the number that would usually be expected on the basis of similar survey
effort across a less-targeted area.
CASE STUDY 2: SPECIES’ DISTRIBUTION MODELING AS A TOOL FOR
PREDICTING INVASIONS OF NON-NATIVE PLANTS (BASED ON THUILLER ET AL.,
2005)
Invasive species are increasingly a global concern, with invasions altering
ecosystem functioning, threatening native biodiversity, and negatively impacting
agriculture, forestry and human health. Species’ distribution modeling can be
used to identify areas that are most likely to be colonized by a known invader.
The general approach is to model the distribution of a species using occurrence
records from its native range, then project the model into new regions to assess
41
susceptibility to invasion. The approach makes use of the type of model
prediction illustrated by area 3 in Figure 3: areas are identified that are part of the
potential, but not actual, distribution. Thuiller et al. (2005) used this method to
identify parts of the world that are potentially susceptible to invasion by plant
species native to South Africa.
Thuiller and colleagues developed distribution models for 96 South African plant
taxa that are invasive in other regions of the globe. Species distribution data
were extracted from large databases of occurrence records that have been
collated for South Africa. Since the surveys incorporated within these databases
were fairly comprehensive, the authors argued that absences within the
databases are reliable and the modeling was thus undertaken using presence
and absence data. Four climate-related variables that are known to affect plant
physiology and growth were developed and used as input to the models. These
included two measures of temperature (growing degree days and temperature of
the coldest month) along with indexes of humidity and plant productivity. All the
analyses were undertaken at a resolution of 25x25 km, which was considered
sufficiently fine to identify environmental differences between regions at a global
scale. Generalized Additive Models (implemented using the Splus-based
BIOMOD application; Table 3) were used to build the distribution models.
The first step in the study was to model each species’ distribution based on its
native range in South Africa. Models were calibrated using 70% of the available
records for each species, with the remaining 30% retained for model testing. The
AUC validation test was applied using presence and absence test data. Because
AUC assesses predictive performance based on continuous model output, it was
not necessary to set a threshold of occurrence. Validation statistics for the test
data were generally very good, with a median AUC score across all 96 species of
0.94 (minimum = 0.68, maximum = 1.0).
The second step in the study was to project the calibrated models worldwide.
The accuracy of the global predictions was assessed for three example species
using presence-only records from their non-native distributions (for example, in
Europe, Australia and New Zealand). Absence records were not available for
these tests, so model performance was assessed using chi-square tests (see
section 5). For each of the species, predictions of potentially suitable areas
outside South Africa showed considerable agreement with observed records of
invasions (chi-square test, P<0.05).
In a further step, Thuiller and colleagues summed the probability surfaces for all
96 taxa to produce a global map for risk of invasion by species of South African
origin. Parts of the world most susceptible to invasion included six biodiversity
‘hotspots’, including the Mediterranean Basin, California Floristic Province, and
southwest Australia. This study demonstrates that species distribution modeling
can be a valuable tool for identifying sites prone to invasion. Such sites may be
42
prioritized for monitoring and quarantine measures can be put in place to help
avoid the establishment of invasive species.
CASE STUDY 3: MODELING THE POTENTIAL IMPACTS OF CLIMATE CHANGE ON
SPECIES’ DISTRIBUTIONS IN BRITAIN AND IRELAND (BASED ON BERRY ET AL.,
2002)
Climate change has the potential to significantly impact the distribution of
species. Species’ distribution models have been used in a number of studies that
aim to predict the likely redistribution of species under projected climate change
over the coming century. The general approach is to calibrate the models based
on current distributions of species and then predict future distributions of those
species across landscapes for which the environmental input variables have
been perturbed to reflect expected changes.
Berry et al. (2002) modeled 54 species that were chosen to represent a range of
habitats common in Britain and Ireland. Species distribution data were obtained
for the whole of Europe (i.e. European extent) from range maps for European
plants, amphibians, butterflies and mammals. Since survey effort across Europe
is generally very high, areas where a species had not been recorded were
considered reliable measures of absence, and both presence and absence data
were therefore used in the modeling. Five environmental variables describing
temperature, precipitation and soil type were used. These variables were
generated using both current climate data and predictions of future climate from
a General Circulation Model (GCM). GCMs are complex simulations that predict
future climates using scenarios of greenhouse gas emissions. The environmental
variables were calculated at a coarse resolution (~50x50km) for Europe, and also
at a finer resolution (10x10km) for Britain and Ireland. The modeling algorithm
was an Artificial Neural Network (Table 3), which gave predictions of relative
suitability ranging from 0 to 1. These continuous predictions were converted into
binary predictions of presence and absence by applying a threshold of
occurrence that maximized the Kappa statistic.
An important part of Berry et al’s (2002) method was that calibration of the
distribution model was carried out at the European scale (large extent and coarse
resolution) and then the model was used to predict distributions in Britain and
Ireland (smaller extent and finer resolution). This approach ensured that when
distributions were predicted under future climate scenarios in Britain and Ireland,
the model was not required to extrapolate beyond the range of data for which it
was calibrated (since future climates in Britain and Ireland are expected to be
similar to conditions currently experienced elsewhere in Europe).
Evaluation of the models was undertaken at the European scale by comparing
model predictions against a test dataset, which comprised one third of the
available data that had been randomly selected and not used in model
calibration. Since both presence and absence records were available, the Kappa
43
statistic was applied. Results from these tests revealed generally good model
performance, with 27 out of 54 species achieving Kappa scores >0.75, and only
7 of 54 species with Kappa scores <0.6.
The models calibrated for Europe were then used to predict distributions in
Britain and Ireland under current and projected future climates. Berry et al.
(2002) emphasized that they did not predict actual distributions, but rather
‘bioclimate envelopes’, or suitable climate space. It is important to remember that
actual future distributions will be determined by many factors that are not taken
into account in the modeling, including the ability of species to colonize areas
that become suitable. Nevertheless, the distribution models enabled each
species to be placed in one of three categories: those expected to lose suitable
climate space, those expected to gain suitable climate space, and those showing
little change. Species’ distribution modeling thus enables preliminary
assessments of the possible impacts of climate change to be made, providing
information that may be valuable in developing conservation policies to address
the threat.
ACKNOWLEDGEMENTS
Thorough comments from five anonymous reviewers greatly improved the
module. The module also benefitted significantly from editorial input by Ian
Harrison and the rest of the NCEP team. Extensive discussions with Robert
Anderson, Catherine Graham, Steven Phillips, Town Peterson, Chris Raxworthy,
Jorge Sóberon and members of the New York Species Distribution Modeling
Discussion Group greatly contributed to the module. I am also indebted to
comments and discussion by participants in courses I have taught through the
American Museum of Natural History, and the Global Biodiversity Information
Facility.
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